Details and Options
Matrix mat has to be numerical.
Median polishing is a robust exploratory data analysis method to find row and column effects in a matrix of data similar to two-way ANOVA. The main idea is that the elements of the matrix are of the form mi,j=c+xi+yj+ϵi,j
. In this model, the xi
are called the row effects
the column effects
the overall effect
and the ϵi,j
are the residuals. In order to estimate these effects, it is assumed that all of these quantities (except the constant c
) average out to 0 over i
. However, since the amount of data is limited, the Mean
is not a good location estimator to use and instead the Median
is used as a more robust alternative. Other location estimators can be specified if necessary.
To estimate c, xi and yj, the algorithm first subtracts the medians from the columns of mat and adds them to the yj and also subtracts the median from the xi vector and adds it to c. Then the algorithm repeats the process for the rows (adding the medians to the xi) and the yj (adding its median to c again). This process is iterated until convergence is reached.
The argument "prop" can either be "Matrix" (default) or "PropertyAssociation".
ResourceFunction["TukeyMedianPolish"] takes the following options:
|"LocationEstimator"||Median||location estimator to use|
|MaxIterations||100||maximum number of iterations to use|
|Tolerance||Scaled[10-4]||maximum (scaled) difference between two successive steps before the algorithm terminates|
|"ConvergenceTest"||Automatic||function that tests if convergence has been reached|
|Compiled||False||whether to use function compilation to speed up the computation|
If a custom "LocationEstimator"
is specified, it should behave in the same way as Median
when applied to a matrix, meaning that locEst[matrix]
should produce the same result as locEst/@Transpose[matrix]
If an option value other than Automatic
is specified for "ConvergenceTest"
, the Tolerance
option will be ignored. The algorithm will evaluate sametest[medians,current]
after each iteration, with medians
being the median values computed in this step and current
being the current output result if the algorithm stops. When the function returns True
, the algorithm stops.